For this section, we are testing and modeling the percent change of the area of glaciers in Glacier National Park with aspect as a factor. The methodology is:
The violin/box plot seems to indicate that an Eastern aspect leads to the smallest percent of area lost, while a Northern aspect leads to the next smallest percent of area lost, and a Northeastern aspect leads to the largest area lost, although the northeastern aspect seems to be distorted by a right-skewed (more larger values) distribution. There also may be some bimodality in the Northeastern distribution, which may mean that there is some unknown split in the Northeastern aspect.
The model output segments the predicted area change by aspect, with:
The observed values and the 80% prediction interval make sense, with only one of the 10 values being outside the prediction interval and the values otherwise being dispersed within the intervals.
For the hypothesis, the p-value for the aspect belonging in the model was .0013, which means that we reject the null hypothesis that the aspect does not have a linear affect on the percent of area change.
The linear model with an aspect as a factor has an RMSE (root mean squared error - a metric where smaller values are better) of 0.42, while a model with just the intercept term has an RMSE of 3.36
The graph of predicted outcome vs. the observed outcome should be roughly linear, which the data appears to be. The slight deviation is likely due to an extremely small test dataset because of the small number of overall observations.